Question: Does my privacy policy have to change if I use Full Site Editing blocks?
Answer: No. It shouldn’t need to change.
What if I start using the Post Comments blocks and hadn’t supported comments in my previous theme.
Ah, well that might make a difference!
PS. Did you know that WordPress supports a privacy policy template? If your page is marked as the “Privacy policy” page then it will look for that first. It’s not listed in Template hierarchy